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All the (relevant) Answers in Mathematical Finance
Stochastic Integration and Differential Equations: Version 2.1: A New Approach (Stochastic Modelling and Applied Probability)Stochastic Integration and Differential Equations: Version 2.1: A New Approach (Stochastic Modelling and Applied Probability) by Philip E. Protter
Buy new: £55.99 / Used from: £44.88
A radically different approach
Applied Stochastic Control of Jump Diffusions (Universitext)Applied Stochastic Control of Jump Diffusions (Universitext) by Bernt Øksendal
Buy new: £27.79 / Used from: £25.36
Lovely Jumps
Controlled Markov Processes and Viscosity Solutions (Stochastic Modelling and Applied Probability)Controlled Markov Processes and Viscosity Solutions (Stochastic Modelling and Applied Probability) by Wendell H. Fleming
Buy used from: £47.38
Modern Control Theory
Deterministic and Stochastic Optimal Control (Stochastic Modelling and Applied Probability)Deterministic and Stochastic Optimal Control (Stochastic Modelling and Applied Probability) by Wendell H. Fleming
Buy used from: £57.00
Classic Approach to Control Theory
Methods of Mathematical Finance (Stochastic Modelling and Applied Probability)Methods of Mathematical Finance (Stochastic Modelling and Applied Probability) by Ioannis Karatzas
Buy new: £54.33 / Used from: £31.40
Definitive Classical Approach to Financial Mathematics
Brownian Motion and Stochastic Calculus (Graduate Texts in Mathematics)Brownian Motion and Stochastic Calculus (Graduate Texts in Mathematics) by Ioannis Karatzas
Buy new: £39.08 / Used from: £29.76
Looks far worse than it is....
Diffusions, Markov Processes and Martingales (Volume 1): Foundations v. 1 (Cambridge Mathematical Library)Diffusions, Markov Processes and Martingales (Volume 1): Foundations v. 1 (Cambridge Mathematical Library) by L. C. G. Rogers
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Truely understanding just a fraction of this would be enough for a whole academic career
Diffusions, Markov Processes and Martingales: Volume 2, Itô Calculus: Ito Calculus v. 2 (Cambridge Mathematical Library)Diffusions, Markov Processes and Martingales: Volume 2, Itô Calculus: Ito Calculus v. 2 (Cambridge Mathematical Library) by L. C. G. Rogers
Buy new: £33.25 / Used from: £25.99
Truely understanding just a fraction of this would be enough for a whole academic career
Probability with Martingales (Cambridge Mathematical Textbooks)Probability with Martingales (Cambridge Mathematical Textbooks) by David Williams
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Basics
Stochastic Differential Equations: An Introduction with Applications (Universitext)Stochastic Differential Equations: An Introduction with Applications (Universitext) by Bernt Oksendal
Buy new: £24.01 / Used from: £30.33
An introduction or for when the others make me depressed and I need to feel intelligent again!
Statistics of Random Processes: General Theory v. 1: I. General Theory (Stochastic Modelling and Applied Probability)Statistics of Random Processes: General Theory v. 1: I. General Theory (Stochastic Modelling and Applied Probability) by Robert S. Liptser
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Everything a girl needs to know about Filtering (and a few things she doesn't)
Statistics of Random Processes: Applications v. 2 (Stochastic Modelling and Applied Probability): II. ApplicationsStatistics of Random Processes: Applications v. 2 (Stochastic Modelling and Applied Probability): II. Applications by Robert S. Liptser
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More Filtering
Financial Modelling with Jump Processes (Chapman & Hall/CRC Financial Mathematics Series)Financial Modelling with Jump Processes (Chapman & Hall/CRC Financial Mathematics Series) by Rama Cont
Buy new: £58.89 / Used from: £73.63
Finance with Jumps
Stochastic Modeling Of Electricity And Related Markets (Advanced Series On Statistical Science & Applied Probability)Stochastic Modeling Of Electricity And Related Markets (Advanced Series On Statistical Science & Applied Probability) by Fred Espen Benth (University of Oslo
Buy new: £56.22 / Used from: £70.69
Electricity Models
Electricity Markets: Pricing, Structures and Economics (The Wiley Finance Series)Electricity Markets: Pricing, Structures and Economics (The Wiley Finance Series) by Chris Harris
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More Electricity
Modelling Prices in Competitive Electricity Markets (The Wiley Finance Series)Modelling Prices in Competitive Electricity Markets (The Wiley Finance Series)
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Yet More Electricity
Carbon Finance: The Financial Implications of Climate Change (Wiley Finance)Carbon Finance: The Financial Implications of Climate Change (Wiley Finance) by Sonia Labatt
Buy new: £34.91 / Used from: £47.14
Carbon Finance